High-pressure studies of a biphasic NiTiSn/Ni2TiSn Heusler alloy by in situ X-ray diffraction and first principle calculations.

Highlights

• The structural behavior of a Heusler alloy was investigated as a function of pressure by XRD combined with DFT calculations.

• The high-pressure behavior of the full-Heusler component was investigated for the first time.

• Pressure induces Ni₃Sn₄ growth at the expense of the possible interfacial component.

Abstract

The present work studies the effect of hydrostatic pressure on a biphasic Heusler alloy using in situ X-ray diffraction. A nanostructured biphasic NiTiSn/Ni₂TiSn Heusler alloy was synthesized by four hours of mechanical alloying using a vibrational high-energy mill and characterized by x-ray diffraction measurements and Rietveld method. The sample was submitted to high-pressure conditions (up to 11.9 GPa) using a diamond anvil cell (DAC) loaded with He, and the structural evolutions were followed by in situ synchrotron x-ray diffraction. The results validate the stability of the half and full-Heusler alloys, as no pressure-induced structural phase transition was observed over the entire pressure range. The behavior of the crystallographic parameters, equation of state and the compressibility factors for both the Heusler phases were obtained from the experimental results as well from the density functional theory (DFT) calculations. The second-order Birch–Murnaghan equation of state determined from our experimental results yields bulk moduli of 143(9) GPa and 156(6) GPa for the Half and Full Heusler phases, respectively. According to the DFT calculations, the corresponding values are 131.0(9) GPa and 161.8(8) GPa.

Introduction

Over the last few decades, the crystallization of the NiTiSn and Ni₂TiSn compounds as half-Heusler (HH) and full-Heusler (FH) alloys have gained increasing attention, mainly due to its promising thermoelectric characteristics with excellent electrical properties[1] [2], good mechanical robustness [3] and high thermal stability [4]. These materials are composed of non-expensive, abundant and non-toxic elements [5] that can be easily synthesized by green routes such as standard solid-state methods [4], [6], arc melting, rapid solidification and open die pressing [7], combination of arc-melting, ball-milling and spark plasma sintering [8], mechanical alloying [9], [10] among others.

The performance of a thermoelectric material might be improved if its thermal conductivity is reduced without a strong degradation of its electrical properties. In general, structural and chemical defects play an important role as phonon scattering centers, contributing to the reduction of thermal conductivity. For example, in a recent theoretical study, Dey and Dutta [11] were able to understand the origin of the long-standing discrepancy between ab initio prediction and experimental results on the type of conductivity in these alloys considering the interstitial defects in HF systems (NbCoSn, TiCoSb, and NiTiSn). In the same way, Dasmahapatra et al.[12], using a more realistic model and considering interstitial defects, explained the low band gap of NiTiSn and showed that the power-factor was almost twice of that of the defect-free NiTiSn.

Experimentally, the thermal conductivity has been shown to be sensitive to microstructure (crystallites sizes and microstrains), grain boundaries [13], stoichiometric variations, vacancies, occupation of crystallographic sites, doping and secondary phases [7] which in turn is directly linked to the synthesis method [5], [14], [15], [16], [17], [18], [19]. For example, a reduction between 10% and 30% in thermal conductivity with increase of 50% in the electrical conductivity was reported for a biphasic bulk alloy, composed of Ni₂TiSn and NiTiSn, prepared by induction levitation melting process and this phenomenon was attributed to the NiTiSn/Ni₂TiSn interfacial scattering [20]. In a similar way, the reported improvement in the electrical power factor of a nanosized half-Heusler NiTiSn alloy, produced by milling and sintering [21], was attributed to the existence of Ni₂TiSn nanoprecipitates [15]. Another recent work on a biphasic Nb-Co-Sn system consisting of NbCo₂Sn full Heusler precipitates embedded in a NbCoSn half Heusler matrix [13] showed that the improvement in the thermoelectric properties were related to phonon scattering in misfit defects on the HH/FH interfaces [13].

An easy way to obtain these alloys, in a nanostructured form, with high defect concentration and grain boundaries, is the mechanical alloying (MA). MA involves milling of a solid powder with high mechanical energy provided by the high frequency collisions between hard metallic spheres and the sample particles. MA is a particularly interesting solid-state reaction technique that is able to produce a large amount of metastable phases [22] like nanocrystals [23], supersaturated solid solutions [24] and amorphous alloys [25]. It is difficult to assess the exact role of high energetic collisions in the solid-state reactions mechanism as it depends on many variables [26] which occasionally invokes criticism of the efficacy of MA technique [27]. However, it has been successfully used over the years to synthesize a number of mechanically alloyed multiphase and even single phase nanostructured materials [9], [27], [28], [29], [30].

In one of our previous studies [31], we investigated the pressure dependencies of the structural and thermoelectric properties of the half-Heusler NiTiZ (Z = Si, Ge, Sn and Sb) alloys using the first-principle density functional study. It is important to note that among the above alloys, the half-Heusler NiTiSn demonstrates the highest dimensionless figure of merit. The value of bulk modulus of NiTiSn (B₀ =133(9)GPa), calculated from a second-order Birch Murnaghan equation of state, was found to be in excellent agreement with other theoretically calculated values such as B₀ = 147.81 GPa [32][33], B₀ = 145.81GPa [34] and B₀ = 152.67GPa [34]. These discrepancies between theoretical values could be understood as the consequence of different calculation methods and variables considered. However, a recent high pressure experimental study [35] has reported a considerably smaller bulk modulus (B₀ =119.(4) GPa) [35] for half-Heusler NiTiSn compound, which is in good agreement with that obtained by using the density functional perturbation theory (DFPT):B0 = 114 GPa [36].

In this work we synthesized a two-phase (FH and HH) Ni-Ti-Sn alloy via mechanical alloying technique, using a vibrational high-energy mill. The synthesized sample was then subjected to high pressures up to 11.9 GPa and studied by in situ x-ray diffraction and Rietveld refinement methods. The crystalline evolution with pressure was investigated by DFT and the compressibility coefficients were obtained by the second-order Birch Murnaghan equation.